A novel speculation game with higher reproducibility of stylized facts for financial markets

Kei Katahira, Yu Chen

The financial time series of asset returns have several qualitative properties such as volatility clustering and heavy tails, collectively called stylized facts [1]. They are quite nontrivial features and observed in studies of different markets and instruments.

The reproducibility of the stylized facts is the prerequisite for a market model. However, despite the qualitative properties, they are so constrained that it is not easy to reproduce even with an ad hoc stochastic process. There are some successful procreative models such as GARCH process, yet most currently existing models fail to reproduce all the stylized properties at once.

The situation in agent-based models is similar; for example, Grand Canonical Minority Game [2] can reproduce only 2~3 of the stylized facts. Thereby, this research proposes a novel agent-based model named “Speculation Game” which has the better reproducibility of the stylized facts, making used of the structure of Minority Game.

Speculation Game is a repeated game where players in a game market compete with each other to increase their investing cash by yielding capital gains through round-trip trades. Roughly speaking, this new model has three remarkable differences from previously advocated agent-based models for the financial market: the existence of holding periods, strategic evaluation with capital gains and losses, and allowance of an order with variable quantities.

Multi-agent simulation with Speculation Game can reproduce 8 out of 11 stylized facts reported by Cont [1] under the same parameter setting. Moreover, introducing knowledge from behavioral economics or heterogeneity of players to the model may sufficiently reproduce the rest of three stylized facts.